We construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation (DNLS) for small data in 2 and we show these measures to be absolutely continuous with respect to the Gaussian measure. The key ingredient of the proof is the analysis of the gauge group of transformations associated to DNLS. As an intermediate step for our main result, we prove quasi-invariance with respect to the gauge maps of the Gaussian measure on 2 with covariance (+(−Δ))−1 for any ⩾2
Invariant measures for the periodic derivative nonlinear Schrödinger equation / Genovese, Giuseppe; Lucà, Renato; Valeri, Daniele. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 374:3-4(2018), pp. 1075-1138. [10.1007/s00208-018-1754-0]
Invariant measures for the periodic derivative nonlinear Schrödinger equation
Valeri, Daniele
2018
Abstract
We construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation (DNLS) for small data in 2 and we show these measures to be absolutely continuous with respect to the Gaussian measure. The key ingredient of the proof is the analysis of the gauge group of transformations associated to DNLS. As an intermediate step for our main result, we prove quasi-invariance with respect to the gauge maps of the Gaussian measure on 2 with covariance (+(−Δ))−1 for any ⩾2| File | Dimensione | Formato | |
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